Gilgamesh, also known as Bilgames in early Sumerian texts, was the fifth king of Uruk. This places his reign around 2500 BC and, according to a Sumerian list of kings, reigned for 126 years. In the Tummal Inscription, Gilgamesh, and his son Urlugal, rebuilt the sanctuary of the goddess Ninlil, in Tummal, a sacred quarter in her city of Nippur. In Mesopotamian mythology, he is demigod (two-thirds god and one-third man) with superhuman strength. He used this strength to build walls of Uruk and traveled to meet Utnapishtim, survivor of the Great Deluge.
In Mesopotamian Mythology
In the Epic of Gilgamesh
In the Epic of Gilgamesh, Gilgamesh is a defeater of monsters to gain fame, and later seeks the sage Utnapishtim for the answers to eternal life. He embarks on this journey after his beloved companion, Enkidu, dies.
When Gilgamesh confronts Utnapishtim after a long journey, he observes that Utnapishtim is nothing but an ordinary man and questions the reasoning behind his immortality. Utnapishtim tells how he had survived the Deluge, the worldwide flood sent from the gods because of their dissaproval of Man. The god Ea had told him to construct a boat for his family, his craftsmen, the "animals of the field", and for himself. Ishtar and the rest of the gods wept and regretted the decision to flood the earth. Utnapishtim made a sacrifice to the gods and the smell attracted the gods to the boat. The god of the wind Enlil arrived, enraged that there were survivors, she condems him for instigating the flood. Ea also castigates him for sending a disproportionate punishment. Enlil blesses Utnapishtim and his wife, and rewards them with eternal life.
The main point seems to be that when Enlil granted eternal life it was a unique gift. He demonstrated this point by challenging Gilgamesh to stay awake for six days and seven nights. Gilgamesh could not overcome this challenge and returned back to Uruk with Urshanabi, Utnapishtim's ferryman.
As they are leaving, Utnapishtim's wife asks him to offer a parting gift. Utnapishtim tells Gilgamesh that at the bottom of the sea there lives a boxthorn-like plant that will make him young again. Gilgamesh, by binding stones to his feet so he can walk on the bottom, manages to obtain the plant. He intends to test it on an old man when he returns to Uruk. Unfortunately, when Gilgamesh stops to bathe, it is stolen by a serpent, who sheds its skin as it departs. Gilgamesh weeps at the futility of his efforts, because he has now lost all chance of immortality. He returns to Uruk, where the sight of its massive walls prompts him to praise this enduring work to Urshanabi.
Epic of Gilgamesh on Wikipedia